I agree that there probably isn't much in the way of anything 'full time' about being a lawyer in the wizarding world. However, Dumbledore is on the Wizengamot, and he's allowed to defend Harry, so does that make him a 'lawyer' in the wizarding world? I would imagine that, to be on the Wizengamot, you must have some type of legal training. I originally think that the Wizengamot was made up of only pureblood wizards, but at some point, this changed, and there might be some type of legal training one must do to get into the Wizengamot.
Given the the small population of the wizarding world, and the fact that even in war times the Wizengamot seems to be made up of part-time members with other jobs as their mainstay (Dumbledore, Fudge, arguably Madam Bones, Umbridge, etc), and the fact that most trials seem to be VERY short, law doesn't seem like something that people could make a living from.